The present invention relates to a voltage-controlled oscillator which can perform frequency modulation.
A voltage-controlled oscillator (to be referred to as a VCO hereinafter) is used for reference frequency oscillation of various electronic circuits. When the VCO is used for reference frequency oscillation of a radio transmitter/receiver, an oscillation center frequency must be controlled by a control voltage and an oscillation frequency must be deviated by a modulation signal, thereby performing frequency modulation (to be referred to as FM hereinafter). In this case, an arrangement shown in FIG. 9 is generally used.
That is, a resonant circuit 2 consisting of an inductance coil and a capacitor is excited by a negative resistance generator 1 consisting of active elements, thereby oscillating a frequency determined by a resonant frequency of the resonant circuit 2. A first series circuit consisting of a first capacitor Cc and a first variable capacitance diode (to be referred to as a VCD hereinafter) Dv and a second series circuit consisting of a second capacitor Cs and a second VCD.multidot.Df are connected in parallel with the resonant circuit 2. A control voltage Vc is applied from a terminal 3 to the VCD.multidot.Dv to change the resonant frequency of the resonant circuit 2, and a modulation signal Vm is supplied from a terminal 4 to the VCD.multidot.Df to change the resonant frequency of the resonant circuit 2. That is, the oscillation frequency is controlled by the control voltage Vc, and FM is performed by the modulation signal Vm.
FIGS. 10(A) and 10(B) show equivalent circuits of FIG. 9, in which FIG. 10(A) shows elements for determining the oscillation frequency and FIG. 10(B) shows a synthetic state of the elements. Assuming that a capacitance of the VCD.multidot.Df is Cf, that an invariable component corresponding to a DC component of the modulation signal Vm is C.sub.0, and that a variable component corresponding to an AC component of the signal Vm is .DELTA.C, Cf=C.sub.0 +.DELTA.C. Assuming that a capacitance of the VC.multidot.Dv is Cv, that an inductance and a capacitance which constitute the resonant circuit 2 are L and C, respectively, and that a synthetic capacitance connected to both ends of the inductance L is Ct, Ct is given by the following equation: ##EQU1##
Assuming that oscillation frequency for .DELTA.C=0 is f.sub.0, oscillation frequency f determined by the above equations is represented by the following equation: ##EQU2##
Since equation (2) is a function of .DELTA.C, this equation is subjected to Taylor expansion to obtain the following equation: ##EQU3##
Assuming that f=f.sub.0 +.DELTA.f, frequency deviation .DELTA.f is represented by the following equation: ##EQU4##
The characteristic of the VCD.multidot.Df is Cf =K.multidot.V.sup.-r as is well known. Assume that an invariable component of the modulation signal Vm is V.sub.0, that a variable component thereof is .DELTA.V, and that Vm=V.sub.0 +.DELTA.V. In this case, since Cf=C.sub.0 +.DELTA.C, the following equation is obtained: ##EQU5## In this case, since C.sub.0 is a capacitance obtained when .DELTA.V=0, C.sub.0 =K.multidot.V.sub.0.sup.-r is obtained. Therefore, the following equation is obtained: ##EQU6##
A substitution of equation (5) into equation (4) yields frequency deviation .DELTA.f near only V.sub.0 as follows: ##EQU7## Therefore, modulation sensitivity S is represented as the following equation: ##EQU8## When a and b of equation (1) are substituted into equation (6), the following equation is obtained: ##EQU9##
When a relationship between Cp and f.sub.0 obtained from equation (3) is substituted into equation (7), the following equation is obtained: ##EQU10##
Therefore, the modulation sensitivity S is increased in proportion to the third power of the center oscillation frequency f.sub.0.
However, when the oscillation frequency f.sub.0 is used as a reference of a carrier frequency, the modulation frequency varies in accordance with it. Therefore, if a conventional VCO is used, modulation sensitivities of channels having different frequencies are, not undesirably, uniform.